The fit to the shock Hugoniot can be used to predict the
mechanical equation of state, using the Hugoniot as a reference curve
[1]}
\(p(\rho ,e) & = & p_r(\rho ) + \Gamma (\rho )\left[e - e_r(\rho )\right] \\p_r(\rho ) & = & \dfrac{c_0^2\rho _r\rho (\rho -\rho _r)}{\left[\rho +s_1(\rho -\rho _r)\right]^2} \\e_r(\rho ) & = & e_0 + \frac{1}{2} p_r(\rho )\left(\frac{1}{\rho _r}-\frac{1}{\rho }\right),\) 
